{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T18:47:55Z","timestamp":1788634075220,"version":"build-2803163510"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,9]],"date-time":"2020-02-09T00:00:00Z","timestamp":1581206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we present a robust algorithm to solve numerically a family of two-dimensional fractional integro differential equations. The Haar wavelet method is upgraded to include in its construction the Laplace transform step. This modification has proven to reduce the accumulative errors that will be obtained in case of using the regular Haar wavelet technique. Different examples are discussed to serve two goals, the methodology and the accuracy of our new approach.<\/jats:p>","DOI":"10.3390\/a13020037","type":"journal-article","created":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T11:48:51Z","timestamp":1581335331000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["New Numerical Treatment for a Family of Two-Dimensional Fractional Fredholm Integro-Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1990-1928","authenticated-orcid":false,"given":"Amer","family":"Darweesh","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Jordan University of Science &amp; Technology, Irbid 22110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marwan","family":"Alquran","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Jordan University of Science &amp; Technology, Irbid 22110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Khawla","family":"Aghzawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Jordan University of Science &amp; Technology, Irbid 22110, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1137\/1031129","article-title":"Continuous and discrete wavelet transforms","volume":"31","author":"Heil","year":"1989","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Daubechies, I. 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